David L Miller
Models that look like:
\[ y_i = \beta_0 + x_{1i}\beta_1 + x_{2i}\beta_2 + \ldots + \epsilon_i \]
(describe the response, \( y_i \), as linear combination of the covariates, \( x_{ji} \), with an offset)
We can make \( y_i\sim \) any exponential family distribution (Normal, Poisson, etc).
Error term \( \epsilon_i \) is normally distributed (usually).
lm(y ~ x1 + poly(x1, 2), data=dat)
lm(y ~ x1 + poly(x1, 2), data=dat)
\[ y_i = \beta_0 + \sum_j s_j(x_{ji}) + \epsilon_i \]
where \( \epsilon_i \sim N(0, \sigma^2) \), \( y_i \sim \text{Normal} \) (for now)
Remember that we're modelling the mean of this distribution!
Call the above equation the linear predictor
\[ \int_\mathbb{R} \left( \frac{\partial^2 f(x)}{\partial^2 x}\right)^2 \text{d}x\\ \]
More on this in a bit…
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